The Phuctoring
trilema.com
trilema.com
To sum it up:
* If you do a batch gcd / mining ps and qs attack on the pgp keyserver data you will find a bunch of broken keys. However most of them are not valid keys, they are just broken copies of valid keys with errors in them. I don't know why they exist, but most likely either due to data transmission errors, disk failures or software bugs. But they don't pose any risk. Their self-signature is invalid, therefore gpg won't use them.
* There are two very old keys that can really be broken with this attack. According to what I know and heard from other people researching this stuff they were created with a no longer developed email encryption tool called CryptoEx by a no longer existing company called Gluck&Kanja. (afaik this hasn't been public knowledge, so I'm dropping it here)
This has been researched before by Arjen Lenstra, Nadia Heninger and myself: https://eprint.iacr.org/2012/064 https://factorable.net/ https://eprint.iacr.org/2015/262.pdf (On the factorable webpage there is an efficient free implementation of this attack by Nadia Heninger - in case you want to play with it)
Other related articles are in their "breaking news" category: http://trilema.com/category/breaking-news/
By the way, I just noticed I'm on their very first list, but I never got the promised email.
Have you tried emailing them to test your theory?
Not really data, but interesting nonetheless to OP's point (and, if true, a little more ammo in my disliking-keyservers gun).
The real data is how often the exponent 281479271743489 appears on that page. That really points toward bugs in key generation, IMO. Bad gpg at some point?
Was this it? http://domino.research.ibm.com/tchjr/journalindex.nsf/0b9bc4...
http://www.ida.liu.se/labs/eslab/SNDFT/docs/IBMdram.pdf "This clearly indicates that because of cosmic rays, for every 256 Mbytes of memory, you'll get one soft error a month," said Tim Dell, senior design engineer for IBM Microelectronics. "The same phenomenon for hard errors with multiple bits will also come into effect with soft errors."
[1] http://spectrum.ieee.org/computing/hardware/how-to-kill-a-su...
Why doesn't the key server scan for this and reject them?
Explanation: https://news.ycombinator.com/item?id=9561179
What they keep finding is: keys that do not pass the first sanity test (very non-standard values and values which most likely come from memory corruption) and keys that share primes with other keys (most likely generated by broken or badly initialised PRNGs).
The same class of issues has been found before on SSL certificates and SSH keys. (https://factorable.net/index.html)
It will get interesting people with affected keys can report back how they generated them and find something in common - maybe specific version of PGP / GPG was broken. You can submit your key via http://phuctor.nosuchlabs.com/ if you want to check your own key quickly.
How do you reason?